Question 122099
The general equation for a circle with center (h,k) and radius, r, is,
{{{(x-h)^2+(y-k)^2=r^2}}}
What is the radius and center of a circle with the equation {{{x^2+y^2=100}}}?
Compare the terms to the general equation. 
{{{(x-h)^2=x^2}}}
{{{h=0}}}
{{{(y-k)^2=y^2}}}
{{{k=0}}}
{{{r^2=100}}}
{{{r=10}}}

The center is({{{0}}},{{{0}}}), radius {{{10}}}
What is the radius and center of a circle with the equation {{{(x-4)^2+y^2=25}}}?
The center is({{{4}}},{{{0}}}), radius {{{5}}}
What is the radius and center of a circle with the equation {{{(x+5)^2+(y-3)^2=18}}}?
The center is({{{-5}}},{{{3}}}), radius {{{sqrt(18)}}}
The next two require you to "complete the square" in both x and y and then compare it to the general form. 
What is the radius and center of a circle with the equation {{{x^2+y^2+4*x-2*y=4}}}?
{{{x^2+y^2+4x-2y=4}}}
{{{x^2+4x+y^2-2y=4}}}
{{{(x^2+4x+4)+(y^2-2y+1)=4+4+1}}}
{{{(x+2)^2+(y-1)^2=9}}}
The center is({{{-2}}},{{{1}}}), radius {{{3}}}
What is the radius and center of a circle with the equation {{{x^2+y^2=2x+10y+25=0}}}
{{{x^2-2x+y^2-10y=25}}}
{{{(x^2-2x+1)+(y^2-10y+25)=25+1+25}}}
{{{(x-1)^2+(y-5)^2=51}}}
The center is({{{1}}},{{{5}}}), radius {{{sqrt(51)}}}